A 2πsolid angle-based heuristic framework for non-coplanar VMAT in multiple brain metastases

Objective.This study proposes a 2πsolid angle-based heuristic framework for non-coplanar volumetric modulated arc therapy (VMAT) in patients with multiple brain metastases (MBM) to automate treatment angle selection.Approach.Fifty-two patients with MBM (2-8 targets) were retrospectively included. A hybrid heuristic framework was constructed: first, a volume-weighted cumulative tumor-skin distance (VW-CTSD) metric was introduced to quantify geometric requirements in the 2πsolid angle space and to automatically identify non-coplanar trajectories minimizing normal brain exposure. Subsequently, a blocking factor-based sub-arc segmentation and collimator-angle selection strategy determined the sub-arc splitting and collimator angles. Using 30 Gy/5 fractions, three plans were generated for each patient: manual expert planning (P_ref), VW-CTSD-guided trajectory selection alone (P_tsd), and the proposed combined heuristic strategy (P_com). Dosimetric metrics and plan parameters were compared.Main results.All plans met clinical goals.P_tsdachieved automated trajectory selection with plan quality comparable toP_ref. Values are presented as median (P25-P75). Compared withP_ref,P_comimproved CI [0.86 (0.85-0.89) to 0.89 (0.85-0.91)] and reduced GI [3.37 (3.17-3.79) to 3.09 (2.74-3.48)].P_comalso reduced normal brain tissue (NBT)V_12Gy, MU, and CM from 92.45 (62.54-141.46) to 83.57 (50.30-125.10) cc, from 2391 (2144-2527) to 1938 (1845-2085), and from 0.22 (0.21-0.24) to 0.20 (0.19-0.21), respectively. Control-point aperture analysis showedX-axis narrowing [129.75 (110.60-146.35) to 101.91 (83.34-120.20) mm] andY-axis expansion [98.70 (80.13-105.86) to 119.17 (103.38-133.48) mm] inP_com. AllP_com-versus-P_refcomparisons for these metrics were statistically significant (P< 0.001).Significance.The proposed combined heuristic framework reduced NBT dose, GI, MU, and CM, suggesting its potential as a practical automated approach for non-coplanar VMAT angle selection in patients with MBM.